Thermionic RF guns are widely used as highly brilliant electron source for linac-driven oscillator FEL (free electron laser). They can potentially produce an electron beam with high energy, small emittance, inexpensive and compact configuration in comparison with other high brightness electron sources. The most critical issue of the thermionic RF gun is the transient cathode heating problem due to the electron backbombardment when the gun is used for an FEL driver. The heating property of cathode not only depends on the emission properties of the cathode material, but also the physical properties such as electron stopping power and range. We investigated the heating property of six hexaboride materials against the backbombarding electrons by numerical calculation of the stopping power and range. In this investigation, the emission property of the cathode was taken into account, since high electron emission is required for generation of high brightness electron beam. As a result, cerium hexaboride material has best properties for thermionic RF gun cathode material in the backbombardment effect point of view.